Flywheels have long been used as energy storage devices. Because it is an inertial device governed by the laws of kinetic energy, a flywheel has an energy storage capacity that increases with increasing rotational speed. The energy storage capacity of a flywheel also increases with increasing spinning radius. Spinning radius is equivalent to the physical radius of a circular flywheel, for example. Generally speaking, the energy storage capacity of a flywheel is directly proportional to the square of rotational velocity and to the square of spinning radius.
The maximum energy storage capacity of a flywheel is limited by the specific strength, or ratio of strength to density, of the material used to fabricate the flywheel. In order to produce a flywheel that potentially has a high energy storage capacity, a material with a high specific strength must be used to build the flywheel. The rotational speed and spinning radius or size of the flywheel can then be proportioned relative to each other to maximize the stress or energy stored in the flywheel material without exceeding the ultimate strength of the material. In fixed installations, such as electrical power generating stations, it may be acceptable to have a flywheel that is large in size and rotates at a relatively low velocity. For use in a vehicle, on the other hand, a flywheel may have to be small in size and, therefore, rotate at a high velocity. Since a high energy flywheel should have an energy storage capacity or energy density of at least 10 watt-hours per pound, and preferably 30 or more watt-hours per pound, the rotational speeds required of a small size flywheel (e.g., 12 to 24 inches in radius) to achieve high energy storage capacity are in the range of 10,000 to 100,000 revolutions per minute. Nonetheless, such speeds of a shaft are attainable with presently known drive trains. Consequently, the major problem of current interest is to select materials for a flywheel and so to construct the flywheel that it will attain the highest possible rotational speed without disintegrating or bursting.
In the past, high strength steel has routinely been chosen as the material of which to construct a flywheel. Steel has a specific strength such that the maximum energy storage capacity or energy density of an isotropic steel flywheel is about 2 to 5 watt-hours per pound. More recently, however, anisotropic filamentary materials have been developed which have ratios of uniaxial strength to density that are substantially greater than that of isotropic steel members. As a result, energy storage capacities or energy densities of 120 watt-hours per pound or more are now theoretically possible using such materials. High strength filamentary materials may be wound about a central hub, for example, to produce a circular flywheel. Alternatively, the filaments may be disposed normal to the axis of rotation of the flywheel. When such filamentary elements are disposed normal to the axis of rotation of the flywheel, the filaments may be individually secured to a central hub or they may be bonded together in a matrix material to form a solid or continuous rotor. Substantial work in the field of filamentary flywheel structures has recently been done by David W. Rabenhorst of the Applied Physics Laboratory at The Johns Hopkins University. Mr. Rabenhorst is the inventor or co-inventor of several patented flywheel designs employing filamentary elements, which are described and illustrated in patents such as: Rabenhorst U.S. Pat. Nos. 3,672,241; Rabenhorst 3,698,262; Rabenhorst 3,737,694; Rabenhorst et al 3,788,162; Rabenhorst 3,884,093; and Rabenhorst 3,964,341.
Particularly when nonisotropic, filamentary structures are utilized as flywheels or similar rotors, difficulty is encountered in securely attaching such flywheels or rotors to a drive shaft. One approach, which is illustrated in FIG. 2 of Rabenhorst U.S. Pat. No. 3,884,093 and FIG. 8 of Rabenhorst et al U.S. Pat. No. 3,788,162, is to pierce the flywheel or rotor with either the drive shaft itself or an associated attachment mechanism, such as a rod or bolt. An inherent problem with piercing a flywheel or rotor, however, is that the maximum stresses developed in the flywheel at any rotational speed are significantly increased. An increase in the stresses produced in a flywheel or rotor will correspondingly reduce the maximum speed at which the flywheel may be rotated without bursting. Reduction in the ultimate bursting speed of the flywheel reduces the energy storage capacity of the flywheel.
The foregoing disadvantage which arises from piercing a flywheel to attach it to a drive shaft may be better understood by considering a hypothetical solid flywheel of circular shape and uniform thickness throughout. In such a flywheel, the maximum radial and tangential stresses (S.sub.R and S.sub.T) due to centrifugal force both occur at the center of the flywheel and are equal to each other. The stresses are determined by the following equation: ##EQU1## In equation (1), P is the density of the flywheel material in pounds per cubic inch, .omega. is the rotational velocity of the flywheel in radians per second, .mu. is Poisson's ratio for the flywheel material, and r is the radius of the flywheel in inches. For an identical disc-shaped flywheel having a central opening formed to accept a drive shaft, for example, the tangential stress (S.sub.T.sup.') in the flywheel due to centrifugal force is the critical stress. The maximum tangential stress occurs at the internal circumference of the annular flywheel and is determined by the following equation: ##EQU2## In equation (2), P, .omega. and .mu. have the same meaning as in equation (1), while r.sub.1 is the outer radius of the flywheel in inches and r.sub.2 is the inner radius of the flywheel in inches. By comparing equation (1) with equation (2), it is readily apparent that if the densities, rotational velocities, and outer radii of the two flywheels are equal, placing an opening of any radius or diameter in a flywheel will more than double the maximum stress. Consequently, an annular flywheel will have less than one-half the energy storage capacity of a substantially identical, solid disc-shaped flywheel. Similar calculations can be made for other flywheel or rotor shapes, such as the rod-like rotor shown in FIG. 2 of Rabenhorst U.S. Pat. No. 3,672,241.
Another method of attaching a drive shaft to a flywheel or rotor, which has been used particularly with flywheels fabricated of high strength filamentary elements, is to provide an enlarged flange or hub at one end of the drive shaft and to bond the hub directly to the flywheel or rotor. An example of such an attachment is shown in FIG. 2 of Rabenhorst et al U.S. Pat. No. 3,788,162. Bonding a flywheel to a shaft avoids the reduction in energy storage capacity which results from piercing a flywheel to attach a drive shaft. Nonetheless, testing of flywheels bonded to drive shafts has resulted in repeated failures of the attachment prior to attaining the maximum energy storage capacities of the flywheels being mounted, as represented by the bursting speeds of the flywheels. Such failures at flywheel-hub interfaces have continued to occur despite the use of high strength epoxy-based structural adhesives to bond the flywheels to the hubs.